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When a Minimum Variance Hedge Ratio Exceeds One

Article Quant Q&A · Author: mrhappysmile
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Summary

The document explains that a minimum variance hedge ratio can exceed one. It gives the relationship between the hedge ratio, spot-to-futures price correlation, and the ratio of their price-change standard deviations. Since correlation cannot exceed one, a ratio above one can occur when spot volatility is substantially larger than futures volatility and the correlation is close to its maximum.

The intuition is that lower futures volatility may require a larger futures position to offset variability in the spot exposure. The explanation is qualitative and does not provide a worked calculation, empirical evidence, or guidance on estimating inputs. Its conclusion follows from the stated formula, so the result depends on the chosen assets, measurement period, and reliability of the estimated correlation and volatilities.

Key ideas

  • The minimum variance hedge ratio depends on correlation and the relative standard deviations of spot and futures price changes.
  • A hedge ratio above one is possible when spot volatility is sufficiently greater than futures volatility.
  • High correlation supports the hedge, while a futures contract with much lower volatility may require a larger position.
  • The document gives intuition but no example or empirical validation.

Tags

FuturesRisk managementPosition sizing
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# Can the Minimum Variance Hedge ratio be greater than 1?


# Can the Minimum Variance Hedge ratio be greater than 1?












The Minimum Variance Hedge ratio is defined as: $h = \rho * \frac{\sigma_S}{\sigma_F}$

For correlation $\rho$ and $\sigma_S , \sigma_F$ for S.D. of changes in asset and future prices accordingly.

Can this value h be greater than 1?

## Answer by rhaskett (score 1, accepted)

https://quant.stackexchange.com/a/16645

Yes. Correlations max out at 1. However if the correlation is near 1 and the volatility of the spot is significantly larger than the volatility of the future the hedge ratio will be greater than 1.

The intuition is if that vol of the future is much smaller than the vol of the spot you might need a lot more futures to minimize the high spot variance.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.